/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date:        19. March 2015
* $Revision: 	V.1.4.5
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_mat_inverse_f64.c
*
* Description:	Floating-point matrix inverse.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*   - Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupMatrix
 */

/**
 * @defgroup MatrixInv Matrix Inverse
 *
 * Computes the inverse of a matrix.
 *
 * The inverse is defined only if the input matrix is square and non-singular (the determinant
 * is non-zero). The function checks that the input and output matrices are square and of the
 * same size.
 *
 * Matrix inversion is numerically sensitive and the CMSIS DSP library only supports matrix
 * inversion of floating-point matrices.
 *
 * \par Algorithm
 * The Gauss-Jordan method is used to find the inverse.
 * The algorithm performs a sequence of elementary row-operations until it
 * reduces the input matrix to an identity matrix. Applying the same sequence
 * of elementary row-operations to an identity matrix yields the inverse matrix.
 * If the input matrix is singular, then the algorithm terminates and returns error status
 * <code>ARM_MATH_SINGULAR</code>.
 * \image html MatrixInverse.gif "Matrix Inverse of a 3 x 3 matrix using Gauss-Jordan Method"
 */

/**
 * @addtogroup MatrixInv
 * @{
 */

/**
 * @brief Floating-point matrix inverse.
 * @param[in]       *pSrc points to input matrix structure
 * @param[out]      *pDst points to output matrix structure
 * @return     		The function returns
 * <code>ARM_MATH_SIZE_MISMATCH</code> if the input matrix is not square or if the size
 * of the output matrix does not match the size of the input matrix.
 * If the input matrix is found to be singular (non-invertible), then the function returns
 * <code>ARM_MATH_SINGULAR</code>.  Otherwise, the function returns <code>ARM_MATH_SUCCESS</code>.
 */

arm_status arm_mat_inverse_f64(
    const arm_matrix_instance_f64 *pSrc,
    arm_matrix_instance_f64 *pDst)
{
    float64_t *pIn = pSrc->pData;                  /* input data matrix pointer */
    float64_t *pOut = pDst->pData;                 /* output data matrix pointer */
    float64_t *pInT1, *pInT2;                      /* Temporary input data matrix pointer */
    float64_t *pOutT1, *pOutT2;                    /* Temporary output data matrix pointer */
    float64_t *pPivotRowIn, *pPRT_in, *pPivotRowDst, *pPRT_pDst;  /* Temporary input and output data matrix pointer */
    uint32_t numRows = pSrc->numRows;              /* Number of rows in the matrix  */
    uint32_t numCols = pSrc->numCols;              /* Number of Cols in the matrix  */

#ifndef ARM_MATH_CM0_FAMILY
    float64_t maxC;                                /* maximum value in the column */

    /* Run the below code for Cortex-M4 and Cortex-M3 */

    float64_t Xchg, in = 0.0f, in1;                /* Temporary input values  */
    uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l;      /* loop counters */
    arm_status status;                             /* status of matrix inverse */

#ifdef ARM_MATH_MATRIX_CHECK


    /* Check for matrix mismatch condition */
    if((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols)
            || (pSrc->numRows != pDst->numRows))
    {
        /* Set status as ARM_MATH_SIZE_MISMATCH */
        status = ARM_MATH_SIZE_MISMATCH;
    }
    else
#endif /*    #ifdef ARM_MATH_MATRIX_CHECK    */

    {

        /*--------------------------------------------------------------------------------------------------------------
         * Matrix Inverse can be solved using elementary row operations.
         *
         *	Gauss-Jordan Method:
         *
         *	   1. First combine the identity matrix and the input matrix separated by a bar to form an
         *        augmented matrix as follows:
         *				        _ 	      	       _         _	       _
         *					   |  a11  a12 | 1   0  |       |  X11 X12  |
         *					   |           |        |   =   |           |
         *					   |_ a21  a22 | 0   1 _|       |_ X21 X21 _|
         *
         *		2. In our implementation, pDst Matrix is used as identity matrix.
         *
         *		3. Begin with the first row. Let i = 1.
         *
         *	    4. Check to see if the pivot for column i is the greatest of the column.
         *		   The pivot is the element of the main diagonal that is on the current row.
         *		   For instance, if working with row i, then the pivot element is aii.
         *		   If the pivot is not the most significant of the columns, exchange that row with a row
         *		   below it that does contain the most significant value in column i. If the most
         *         significant value of the column is zero, then an inverse to that matrix does not exist.
         *		   The most significant value of the column is the absolute maximum.
         *
         *	    5. Divide every element of row i by the pivot.
         *
         *	    6. For every row below and  row i, replace that row with the sum of that row and
         *		   a multiple of row i so that each new element in column i below row i is zero.
         *
         *	    7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
         *		   for every element below and above the main diagonal.
         *
         *		8. Now an identical matrix is formed to the left of the bar(input matrix, pSrc).
         *		   Therefore, the matrix to the right of the bar is our solution(pDst matrix, pDst).
         *----------------------------------------------------------------------------------------------------------------*/

        /* Working pointer for destination matrix */
        pOutT1 = pOut;

        /* Loop over the number of rows */
        rowCnt = numRows;

        /* Making the destination matrix as identity matrix */
        while(rowCnt > 0u)
        {
            /* Writing all zeroes in lower triangle of the destination matrix */
            j = numRows - rowCnt;
            while(j > 0u)
            {
                *pOutT1++ = 0.0f;
                j--;
            }

            /* Writing all ones in the diagonal of the destination matrix */
            *pOutT1++ = 1.0f;

            /* Writing all zeroes in upper triangle of the destination matrix */
            j = rowCnt - 1u;
            while(j > 0u)
            {
                *pOutT1++ = 0.0f;
                j--;
            }

            /* Decrement the loop counter */
            rowCnt--;
        }

        /* Loop over the number of columns of the input matrix.
           All the elements in each column are processed by the row operations */
        loopCnt = numCols;

        /* Index modifier to navigate through the columns */
        l = 0u;

        while(loopCnt > 0u)
        {
            /* Check if the pivot element is zero..
             * If it is zero then interchange the row with non zero row below.
             * If there is no non zero element to replace in the rows below,
             * then the matrix is Singular. */

            /* Working pointer for the input matrix that points
             * to the pivot element of the particular row  */
            pInT1 = pIn + (l * numCols);

            /* Working pointer for the destination matrix that points
             * to the pivot element of the particular row  */
            pOutT1 = pOut + (l * numCols);

            /* Temporary variable to hold the pivot value */
            in = *pInT1;

            /* Grab the most significant value from column l */
            maxC = 0;
            for (i = l; i < numRows; i++)
            {
                maxC = *pInT1 > 0 ? (*pInT1 > maxC ? *pInT1 : maxC) : (-*pInT1 > maxC ? -*pInT1 : maxC);
                pInT1 += numCols;
            }

            /* Update the status if the matrix is singular */
            if(maxC == 0.0f)
            {
                return ARM_MATH_SINGULAR;
            }

            /* Restore pInT1  */
            pInT1 = pIn;

            /* Destination pointer modifier */
            k = 1u;

            /* Check if the pivot element is the most significant of the column */
            if( (in > 0.0f ? in : -in) != maxC)
            {
                /* Loop over the number rows present below */
                i = numRows - (l + 1u);

                while(i > 0u)
                {
                    /* Update the input and destination pointers */
                    pInT2 = pInT1 + (numCols * l);
                    pOutT2 = pOutT1 + (numCols * k);

                    /* Look for the most significant element to
                     * replace in the rows below */
                    if((*pInT2 > 0.0f ? *pInT2 : -*pInT2) == maxC)
                    {
                        /* Loop over number of columns
                         * to the right of the pilot element */
                        j = numCols - l;

                        while(j > 0u)
                        {
                            /* Exchange the row elements of the input matrix */
                            Xchg = *pInT2;
                            *pInT2++ = *pInT1;
                            *pInT1++ = Xchg;

                            /* Decrement the loop counter */
                            j--;
                        }

                        /* Loop over number of columns of the destination matrix */
                        j = numCols;

                        while(j > 0u)
                        {
                            /* Exchange the row elements of the destination matrix */
                            Xchg = *pOutT2;
                            *pOutT2++ = *pOutT1;
                            *pOutT1++ = Xchg;

                            /* Decrement the loop counter */
                            j--;
                        }

                        /* Flag to indicate whether exchange is done or not */
                        flag = 1u;

                        /* Break after exchange is done */
                        break;
                    }

                    /* Update the destination pointer modifier */
                    k++;

                    /* Decrement the loop counter */
                    i--;
                }
            }

            /* Update the status if the matrix is singular */
            if((flag != 1u) && (in == 0.0f))
            {
                return ARM_MATH_SINGULAR;
            }

            /* Points to the pivot row of input and destination matrices */
            pPivotRowIn = pIn + (l * numCols);
            pPivotRowDst = pOut + (l * numCols);

            /* Temporary pointers to the pivot row pointers */
            pInT1 = pPivotRowIn;
            pInT2 = pPivotRowDst;

            /* Pivot element of the row */
            in = *pPivotRowIn;

            /* Loop over number of columns
             * to the right of the pilot element */
            j = (numCols - l);

            while(j > 0u)
            {
                /* Divide each element of the row of the input matrix
                 * by the pivot element */
                in1 = *pInT1;
                *pInT1++ = in1 / in;

                /* Decrement the loop counter */
                j--;
            }

            /* Loop over number of columns of the destination matrix */
            j = numCols;

            while(j > 0u)
            {
                /* Divide each element of the row of the destination matrix
                 * by the pivot element */
                in1 = *pInT2;
                *pInT2++ = in1 / in;

                /* Decrement the loop counter */
                j--;
            }

            /* Replace the rows with the sum of that row and a multiple of row i
             * so that each new element in column i above row i is zero.*/

            /* Temporary pointers for input and destination matrices */
            pInT1 = pIn;
            pInT2 = pOut;

            /* index used to check for pivot element */
            i = 0u;

            /* Loop over number of rows */
            /*  to be replaced by the sum of that row and a multiple of row i */
            k = numRows;

            while(k > 0u)
            {
                /* Check for the pivot element */
                if(i == l)
                {
                    /* If the processing element is the pivot element,
                       only the columns to the right are to be processed */
                    pInT1 += numCols - l;

                    pInT2 += numCols;
                }
                else
                {
                    /* Element of the reference row */
                    in = *pInT1;

                    /* Working pointers for input and destination pivot rows */
                    pPRT_in = pPivotRowIn;
                    pPRT_pDst = pPivotRowDst;

                    /* Loop over the number of columns to the right of the pivot element,
                       to replace the elements in the input matrix */
                    j = (numCols - l);

                    while(j > 0u)
                    {
                        /* Replace the element by the sum of that row
                           and a multiple of the reference row  */
                        in1 = *pInT1;
                        *pInT1++ = in1 - (in * *pPRT_in++);

                        /* Decrement the loop counter */
                        j--;
                    }

                    /* Loop over the number of columns to
                       replace the elements in the destination matrix */
                    j = numCols;

                    while(j > 0u)
                    {
                        /* Replace the element by the sum of that row
                           and a multiple of the reference row  */
                        in1 = *pInT2;
                        *pInT2++ = in1 - (in * *pPRT_pDst++);

                        /* Decrement the loop counter */
                        j--;
                    }

                }

                /* Increment the temporary input pointer */
                pInT1 = pInT1 + l;

                /* Decrement the loop counter */
                k--;

                /* Increment the pivot index */
                i++;
            }

            /* Increment the input pointer */
            pIn++;

            /* Decrement the loop counter */
            loopCnt--;

            /* Increment the index modifier */
            l++;
        }


#else

    /* Run the below code for Cortex-M0 */

    float64_t Xchg, in = 0.0f;                     /* Temporary input values  */
    uint32_t i, rowCnt, flag = 0u, j, loopCnt, k, l;      /* loop counters */
    arm_status status;                             /* status of matrix inverse */

#ifdef ARM_MATH_MATRIX_CHECK

    /* Check for matrix mismatch condition */
    if((pSrc->numRows != pSrc->numCols) || (pDst->numRows != pDst->numCols)
            || (pSrc->numRows != pDst->numRows))
    {
        /* Set status as ARM_MATH_SIZE_MISMATCH */
        status = ARM_MATH_SIZE_MISMATCH;
    }
    else
#endif /*      #ifdef ARM_MATH_MATRIX_CHECK    */
    {

        /*--------------------------------------------------------------------------------------------------------------
         * Matrix Inverse can be solved using elementary row operations.
         *
         *	Gauss-Jordan Method:
         *
         *	   1. First combine the identity matrix and the input matrix separated by a bar to form an
         *        augmented matrix as follows:
         *				        _  _	      _	    _	   _   _         _	       _
         *					   |  |  a11  a12  | | | 1   0  |   |       |  X11 X12  |
         *					   |  |            | | |        |   |   =   |           |
         *					   |_ |_ a21  a22 _| | |_0   1 _|  _|       |_ X21 X21 _|
         *
         *		2. In our implementation, pDst Matrix is used as identity matrix.
         *
         *		3. Begin with the first row. Let i = 1.
         *
         *	    4. Check to see if the pivot for row i is zero.
         *		   The pivot is the element of the main diagonal that is on the current row.
         *		   For instance, if working with row i, then the pivot element is aii.
         *		   If the pivot is zero, exchange that row with a row below it that does not
         *		   contain a zero in column i. If this is not possible, then an inverse
         *		   to that matrix does not exist.
         *
         *	    5. Divide every element of row i by the pivot.
         *
         *	    6. For every row below and  row i, replace that row with the sum of that row and
         *		   a multiple of row i so that each new element in column i below row i is zero.
         *
         *	    7. Move to the next row and column and repeat steps 2 through 5 until you have zeros
         *		   for every element below and above the main diagonal.
         *
         *		8. Now an identical matrix is formed to the left of the bar(input matrix, src).
         *		   Therefore, the matrix to the right of the bar is our solution(dst matrix, dst).
         *----------------------------------------------------------------------------------------------------------------*/

        /* Working pointer for destination matrix */
        pOutT1 = pOut;

        /* Loop over the number of rows */
        rowCnt = numRows;

        /* Making the destination matrix as identity matrix */
        while(rowCnt > 0u)
        {
            /* Writing all zeroes in lower triangle of the destination matrix */
            j = numRows - rowCnt;
            while(j > 0u)
            {
                *pOutT1++ = 0.0f;
                j--;
            }

            /* Writing all ones in the diagonal of the destination matrix */
            *pOutT1++ = 1.0f;

            /* Writing all zeroes in upper triangle of the destination matrix */
            j = rowCnt - 1u;
            while(j > 0u)
            {
                *pOutT1++ = 0.0f;
                j--;
            }

            /* Decrement the loop counter */
            rowCnt--;
        }

        /* Loop over the number of columns of the input matrix.
           All the elements in each column are processed by the row operations */
        loopCnt = numCols;

        /* Index modifier to navigate through the columns */
        l = 0u;
        //for(loopCnt = 0u; loopCnt < numCols; loopCnt++)
        while(loopCnt > 0u)
        {
            /* Check if the pivot element is zero..
             * If it is zero then interchange the row with non zero row below.
             * If there is no non zero element to replace in the rows below,
             * then the matrix is Singular. */

            /* Working pointer for the input matrix that points
             * to the pivot element of the particular row  */
            pInT1 = pIn + (l * numCols);

            /* Working pointer for the destination matrix that points
             * to the pivot element of the particular row  */
            pOutT1 = pOut + (l * numCols);

            /* Temporary variable to hold the pivot value */
            in = *pInT1;

            /* Destination pointer modifier */
            k = 1u;

            /* Check if the pivot element is zero */
            if(*pInT1 == 0.0f)
            {
                /* Loop over the number rows present below */
                for (i = (l + 1u); i < numRows; i++)
                {
                    /* Update the input and destination pointers */
                    pInT2 = pInT1 + (numCols * l);
                    pOutT2 = pOutT1 + (numCols * k);

                    /* Check if there is a non zero pivot element to
                     * replace in the rows below */
                    if(*pInT2 != 0.0f)
                    {
                        /* Loop over number of columns
                         * to the right of the pilot element */
                        for (j = 0u; j < (numCols - l); j++)
                        {
                            /* Exchange the row elements of the input matrix */
                            Xchg = *pInT2;
                            *pInT2++ = *pInT1;
                            *pInT1++ = Xchg;
                        }

                        for (j = 0u; j < numCols; j++)
                        {
                            Xchg = *pOutT2;
                            *pOutT2++ = *pOutT1;
                            *pOutT1++ = Xchg;
                        }

                        /* Flag to indicate whether exchange is done or not */
                        flag = 1u;

                        /* Break after exchange is done */
                        break;
                    }

                    /* Update the destination pointer modifier */
                    k++;
                }
            }

            /* Update the status if the matrix is singular */
            if((flag != 1u) && (in == 0.0f))
            {
                return ARM_MATH_SINGULAR;
            }

            /* Points to the pivot row of input and destination matrices */
            pPivotRowIn = pIn + (l * numCols);
            pPivotRowDst = pOut + (l * numCols);

            /* Temporary pointers to the pivot row pointers */
            pInT1 = pPivotRowIn;
            pOutT1 = pPivotRowDst;

            /* Pivot element of the row */
            in = *(pIn + (l * numCols));

            /* Loop over number of columns
             * to the right of the pilot element */
            for (j = 0u; j < (numCols - l); j++)
            {
                /* Divide each element of the row of the input matrix
                 * by the pivot element */
                *pInT1 = *pInT1 / in;
                pInT1++;
            }
            for (j = 0u; j < numCols; j++)
            {
                /* Divide each element of the row of the destination matrix
                 * by the pivot element */
                *pOutT1 = *pOutT1 / in;
                pOutT1++;
            }

            /* Replace the rows with the sum of that row and a multiple of row i
             * so that each new element in column i above row i is zero.*/

            /* Temporary pointers for input and destination matrices */
            pInT1 = pIn;
            pOutT1 = pOut;

            for (i = 0u; i < numRows; i++)
            {
                /* Check for the pivot element */
                if(i == l)
                {
                    /* If the processing element is the pivot element,
                       only the columns to the right are to be processed */
                    pInT1 += numCols - l;
                    pOutT1 += numCols;
                }
                else
                {
                    /* Element of the reference row */
                    in = *pInT1;

                    /* Working pointers for input and destination pivot rows */
                    pPRT_in = pPivotRowIn;
                    pPRT_pDst = pPivotRowDst;

                    /* Loop over the number of columns to the right of the pivot element,
                       to replace the elements in the input matrix */
                    for (j = 0u; j < (numCols - l); j++)
                    {
                        /* Replace the element by the sum of that row
                           and a multiple of the reference row  */
                        *pInT1 = *pInT1 - (in * *pPRT_in++);
                        pInT1++;
                    }
                    /* Loop over the number of columns to
                       replace the elements in the destination matrix */
                    for (j = 0u; j < numCols; j++)
                    {
                        /* Replace the element by the sum of that row
                           and a multiple of the reference row  */
                        *pOutT1 = *pOutT1 - (in * *pPRT_pDst++);
                        pOutT1++;
                    }

                }
                /* Increment the temporary input pointer */
                pInT1 = pInT1 + l;
            }
            /* Increment the input pointer */
            pIn++;

            /* Decrement the loop counter */
            loopCnt--;
            /* Increment the index modifier */
            l++;
        }


#endif /* #ifndef ARM_MATH_CM0_FAMILY */

        /* Set status as ARM_MATH_SUCCESS */
        status = ARM_MATH_SUCCESS;

        if((flag != 1u) && (in == 0.0f))
        {
            pIn = pSrc->pData;
            for (i = 0; i < numRows * numCols; i++)
            {
                if (pIn[i] != 0.0f)
                    break;
            }

            if (i == numRows * numCols)
                status = ARM_MATH_SINGULAR;
        }
    }
    /* Return to application */
    return (status);
}

/**
 * @} end of MatrixInv group
 */
